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Dado cut rack


SilveRx
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It should be strong enough without a vertical center support but I would add a 2x4 front to back in the center span under the plywood just because.

To add depth you can add a piece of 3/4" plywood that cantilevers over the extra 2"

I have seen people with tanks up to 20 gallon longs have the end of the tank extend past their shelving a couple inches with no issue. I personally like to support the perimeter of the tank.

 

 

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I have built all my stands and racks like this. I only put a vertical support if it is 6 feet long. I have a rack that holds three rows of ten gallons with four across, its almost five feet long and no vertical center support. I do have cross pieces, that are where the edges of the tanks are for extra support that way. 

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I'd probably add an extra 2X4 on each corner forming more of an L shaped leg.  Where you've dadoed in the 2X4 for the bottom shelf you've lost some leg strength.  If you've got the wrong wood grain and some force is applied to the side of the loaded stand, I could see one or more legs failing at the shelf level. Adding an extra length of 2X4 to at least the back two legs would help prevent that. (I'd do it on all four as I'm pretty paranoid and don't trust modern lumber.) It's not always that hard to break a full 2X4 these days and one with a chunk taken out is even weaker. It probably won't break the way you have it built, but I'd prefer to be sure it won't break. If you were building a very long rack this type of design is pretty safe, but for a narrower one the potential for failure is a bit larger. You just need one weak leg and the stand collapses. 

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